On second-order conditions in vector optimization

Ginchev Ivan (), Guerraggio Angelo () and Rocca Matteo ()
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Ginchev Ivan: Department of Mathematics, Technical University of Varna, Bulgaria
Guerraggio Angelo: Department of Economics, University of Insubria, Italy
Rocca Matteo: Department of Economics, University of Insubria, Italy

Economics and Quantitative Methods from Department of Economics, University of Insubria

Abstract: Starting from second-order conditions for C 1,1 scalar unconstrained optimization problems described in terms of the second-order Dini directional derivative, we pose the problem, whether similar conditions for C 1,1 vector optimization problems can be derived. We define second-order Dini directional derivatives for vector functions and apply them to formulate such conditions as a Conjecture. The proof of the COnjecture in the case of C1,1 function (called the nonsmooth case) will be given in another paper. The present paper provides the background leading to its correct formulation. Using Lagrange multipliers technique, we prove the COnjecture in the case of twice Fréchet differentiable function (called the smooth case) and show on example the effectiveness of the obtained conditions. Another example shows, that in the nonsmooth case it is important to take into account the whole set of Lagrange multipliers, instead of dealing with a particular multiplier.

Keywords: nonsmooth vector optimization; second-order conditions (search for similar items in EconPapers)
Pages: 13 pages
Date: 2002-10
New Economics Papers: this item is included in nep-ino
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Citations: View citations in EconPapers (1)

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